Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 3 : pp. 635–654
Abstract
Gradient flows with strong anisotropic free energy are difficult to deal with numerically with existing approaches. We propose a stabilized predictor-corrector approach to construct schemes which are second-order accurate, easy to implement, and maintain the stability of first-order stabilized schemes. We apply the new approach to three different types of gradient flows with strong anisotropic free energy: anisotropic diffusion equation, anisotropic Cahn-Hilliard equation, and Cahn-Hilliard equation with degenerate diffusion mobility. Numerical results are presented to show that the stabilized predictor-corrector schemes are second-order accurate, unconditionally stable for the first two equations, and allow larger time step than the first-order stabilized scheme for the last equation. We also prove rigorously that, for the isotropic Cahn-Hilliard equation, the stabilized predictor-corrector scheme is of second-order.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0209
Communications in Computational Physics, Vol. 24 (2018), Iss. 3 : pp. 635–654
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Predictor-corrector anisotropy Cahn-Hilliard equation Willmore regularization degenerate diffusion mobility.